# Virtual Work Method on a Truss

• dtb_419
In summary, the conversation is about using the Virtual Work method to calculate horizontal deflections at joints A and F in a truss structure. The process involves solving member forces, organizing information in a table, and using the Deflection Equation from Virtual Work. The question is how to introduce the unit load in order to calculate the deflections at A and F. It is clarified that the unit load should be applied at each requested joint separately, and the direction of the load does not matter. The final step is to combine the results from both analyses to get the desired deflections.
dtb_419

## Homework Statement

I want to calculate the horizontal deflections at joints A and F (using Virtual Work method taught in Structural Engineering). Cross-Sectional Area (A) and E values are provided in the problem, and the attachment has all relevant dimensions and applied loads.

## Homework Equations

Deflection is 1[k](Δ)=∑(Virtual Force/AE)

## The Attempt at a Solution

So far in class, Virtual Work problems have involved using the Unit Load Method (a hypothetical 1 kip load that can be used to calculate deflection from its effect on a given structure).

The general method (as I understand it, in a truss structure) is this:

1. Solve all member forces.

2. Organize all information (member length in inches, member force, cross-sec area, and MEMBER FORCE FROM UNIT LOADING into a table.

3. Summation of Virtual Forces from table plugged into Deflection Equation from Virtual Work.

Step 1. I've already done myself (joint method), and Step 3. is a matter of plugging in known data from Step 2. No questions there.

Step 2. is where my question is.

This particular question wants horizontal deflections at A and also F. What I think I should do is introduce a horizontal 1 kip load at each of the respective joints, and repeat the joint analysis to reflect this change from the unit load. But in what direction (sign convention) should they be introduced? Should I introduce a horizontal 1 kip load at EACH joint, or only the requested joints?

Some problems I've seen introduce the unit load at only the requested joint, and recalculate all other member forces to adjust for that change (which is what I'm leaning towards doing), but others introduce the unit load immediately, without taking initial member forces. This is confusing, and so I'm asking for a clarification in procedure.

No numbers are necessary. Thanks everyone!

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If you want the deflection at a particular point, apply the unit load there, and only there. The direction doesn't really matter, but if the answer is negative, that means it was the other way. Still correct though. So you have the frame analyzed with the given loads, and secondly, you have the frame analyzed with just the unit load. Do you know how to combine these two results to give you the deflection you want?

Regarding the two results for deflection of A and F, aren't they separate deflections? Like, for A I apply a unit load at A horizontally, and calculate changes in member forces, and multiply in the PL/AE equation eventually? Then do the same thing for F, and have two separate deflections?

I thought that for however many deflections you wanted, you had to have that many virtual structures? Are you saying that I apply a unit load to the truss at A and F at the same time?

Not at the same time. Two separate processes, one for each deflection required. However, there is a matrix method that does it all in one go. But that is not the method you are pursuing here.

I would recommend using the virtual work method to calculate the horizontal deflections at joints A and F. This method is commonly used in structural engineering and can provide accurate results when applied correctly.

In terms of the specific problem, it is important to carefully organize all the information and data, including member forces, cross-sectional area, and applied loads. This will help in accurately calculating the deflections at the requested joints.

In terms of introducing the horizontal 1 kip load, it is important to follow a consistent sign convention. This means that the load should be introduced in the same direction at both joints A and F. Additionally, it is important to consider the effect of the load on all other member forces, not just at the requested joints. This will ensure that the calculations are accurate and take into account all relevant factors.

In summary, I would recommend carefully organizing the information and using a consistent sign convention when introducing the horizontal 1 kip load. Additionally, it is important to consider the effect of the load on all member forces in order to accurately calculate the deflections at joints A and F.

## 1. What is a virtual work method on a truss?

The virtual work method on a truss is a structural analysis technique used to determine the internal forces and displacements in a truss structure. It is based on the principle of virtual work, where external virtual forces are applied to the structure and the corresponding virtual work is calculated to determine the internal forces.

## 2. How does the virtual work method work?

The virtual work method involves creating a virtual model of the truss structure by applying virtual forces to the joints and calculating the corresponding virtual work. This virtual work is then equated to the actual work done by the internal forces in the truss. By solving this equation, the internal forces and displacements in the truss can be determined.

## 3. What are the advantages of using the virtual work method on a truss?

The virtual work method has several advantages, including its ability to handle complex and statically indeterminate truss structures. It also provides accurate results, especially for structures with non-uniform member properties. Additionally, it can be easily programmed and automated, making it a convenient analysis method.

## 4. Are there any limitations to the virtual work method on a truss?

One limitation of the virtual work method is that it assumes linear elastic behavior of the truss members, which may not be accurate for some materials. Additionally, it may be time-consuming to set up the virtual model and solve the resulting equations, especially for large and complex truss structures.

## 5. Can the virtual work method be applied to other types of structures?

Yes, the virtual work method can be applied to other types of structures, such as beams, frames, and even three-dimensional structures. However, the method may need to be modified to account for the specific structural characteristics and loading conditions of each type of structure.

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